Diffusion Model Sampling With Higher-Order ODE Curvature
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Solution Overview
Problem
Denoising diffusion generative models (DDMs) require numerous iterative deep neural network calls for data synthesis, leading to slow sampling and high resource usage, particularly due to the complexity of solving the generative ordinary differential equation (ODE) with first-order solvers.
Innovation Solution
Implementing a higher-order truncated Taylor method (TTM) solver, such as a second-order ODE solver, using a separate neural network to predict higher-order terms, allowing for larger steps and reducing the number of network calls by modeling the local curvature of the ODE gradient field.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Speed
If first-order ODE solvers are used for denoising diffusion generative models, then the model can be implemented with simpler computational steps, but the sampling speed is slow and computational time is excessive
Solution Approach 1:
The patent transitions from static first-order ODE solving to dynamic higher-order ODE solving by introducing time-dependent higher-order derivative terms. The second-order solver dynamically adjusts the denoising trajectory by incorporating curvature information (d²x/dt²) that adapts to the local geometry of the probability flow, enabling faster convergence while maintaining accuracy.
Solution Approach 2:
The patent performs preliminary computation of higher-order score functions and curvature terms during the training phase. These pre-computed higher-order derivatives are then used during sampling to directly guide the denoising process, avoiding the need for iterative first-order solving and enabling larger step sizes from the outset.
2Productivity
If first-order ODE solvers are used, then the implementation is simpler, but the number of deep neural network calls is excessive leading to high resource usage
Solution Approach 1:
The patent extracts and separately models the higher-order derivative terms (curvature, jerk) from the standard first-order ODE framework. By isolating these higher-order components and modeling them with dedicated neural network heads, the system can compute them efficiently in parallel with the main score function, reducing total computation time and resource usage during sampling.
Solution Approach 2:
The patent segments the ODE solving process into multiple independent higher-order derivative computations (first derivative/score function, second derivative/curvature, third derivative/jerk). Each segment is handled by a specialized neural network component, allowing modular computation that reduces redundancy and optimizes resource utilization compared to repeated first-order solving.
3Speed
If higher-order terms are modeled with a separate neural network, then larger steps can be taken in the ODE solving process, but the model complexity increases
Solution Approach 1:
The patent implements higher-order derivative networks as nested components within the main diffusion model architecture. The score function network and curvature network share underlying features and parameters, with higher-order networks nested within the computational graph of the base model. This nested structure allows larger step sizes while managing complexity through parameter sharing and architectural integration.
Solution Approach 2:
The patent designs the higher-order neural network components to serve multiple functions: they compute curvature information for second-order ODE solving, provide regularization during training, and can be adapted for different diffusion schedules. This multi-functionality justifies the increased model complexity by delivering multiple benefits beyond just enabling larger step sizes.
Data Source
AI summary
Approaches presented herein provide for the generation of synthesized data from input noise using a denoising diffusion network. A higher order differential equation solver can be used for the denoising process, with one or more higher-order terms being distilled into one or more separate efficient neural networks. A separate, efficient neural network can be called together with a primary denoising model at inference time without significant loss in sampling efficiency. The separate neural network can provide information about the curvature (or other higher-order term) of the differential equation, representing a denoising trajectory, that can be used by the primary diffusion network to denoise the image using fewer denoising iterations.